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Minitab 15 Tutorial:
Using Power and Sample Size Tools with Power Curves

For any job, you need a tool that offers the right amount of power. You
don’t use a telescope to examine a stamp collection or a handheld magnifying
glass to search for new galaxies because neither provide you with meaningful
observations. To complicate matters, the cost of achieving the necessary
power might be more than you can afford.

Anyone who uses statistical tests faces the same issues. You must consider
the precision that you need to meet your goals (should your test detect
subtle effects or massive shifts?) and balance it against the cost of
sampling your population (are you testing toothpicks or jet engines?).
You also want the confidence in your results that’s appropriate for your
situation (tests for seat belts demand a greater degree of certainty than
tests for shampoo require). We can measure this certainty using statistical
power—the probability that your test will detect an effect that truly exists.

Minitab’s Power and Sample Size tools, with Power Curves, help you to balance
these issues that may compete for your limited resources. Here are three
examples of how a quick Power and Sample Size test can help you to save time
and money, while still providing results that you can trust.

Don’t leave success to chance

A paper clip manufacturer wants to detect significant changes in clip length.
The manufacturer samples thousands of clips because it is cheap and quick to
do. But this huge sample makes the test too sensitive: the red line shows
that the test warns of a change even if the average length differs by a
trivial amount (0.05).

This Power Curve shows that the manufacturer is wasting resources on excessive
precision. A sample size of just 100 will detect meaningful differences
(0.25) without generating a false alarm at every negligible change.

An aerospace company is designing an experiment to test a new rocket. Each
rocket is very expensive, so it is critical to test no more than necessary.

This Power Curve confirms an experiment with 6 replicates will give
researchers the power that they need without spending more than they must.

“We’ve always done it this way.” That’s why workers at a lumber company sample
10 beams to test whether their strength meets the target.

The Power Curve shows that this sample size is too small for the test to detect
important effects. The workers must sample 34 beams for the test to detect
meaningful differences (0.50).

Balancing Priorities

A power analysis helps you to weigh your resources against your demands and
quantifies a test’s ability to answer your question. It can expose design
problems, like the lumber company’s insufficient sample size. It can also
reveal design solutions that you haven’t considered.

Take, for example, the packaging plant of a snack company. Customers complain
that the company’s pretzel bags are sealed with glue that’s too strong, so
researchers use One-Way ANOVA to compare their current glue with three
potential replacements. Differences in seal strength that are less than 10
are undetectable to most people, so the test needs to detect a difference of
only 10. A power value of 80% is acceptable, but 90% is ideal. What sample
size meets the researchers’ needs?

30 samples of each glue ensure that the test detects a difference of 10
with 90% power.

Or, the researchers could detect the same difference with 23 samples and 80%
power. If this represents a considerable savings, the researchers may consider
using the smaller sample.

The Power Curve illustrates this information, but it also charts every other
combination of power and difference for a given sample size.

The black line indicates that researchers can attain 90% power with just 23
samples if they are willing to seek a difference of 12 instead of 10. This
might be the ideal choice.

How to create Power Curves in Minitab

Performing power analyses with Power Curves couldn’t be simpler. Supply the
factors that you know, and Minitab calculates the one that you omit.

Suppose a trainer wants to compare two training courses for forklift
operators. She will use a 2-sample t-test to compare the average scores that
operators from each course earn on the final exam. She knows that she must
be able to detect a difference of 5 between the two courses with 80% power,
and historical data suggest a standard deviation of 5. But how many
participants must she sample from each course?

Choose Stat > Power and Sample Size > 2-Sample t.

In Differences, type 5.

In Power values, type 0.80.

In Standard deviation, type 5.

Click OK.

This Power Curve indicates that the trainer must sample 17 participants from
each class for her test to detect the difference that she seeks with 80% power.

Putting Power Curves to use

If you don’t know the power of your test, it’s hard to know whether you can
trust your results: your test could be too weak to answer your question or
too strong for your needs. Minitab’s Power Curves (available for many common
statistical procedures) help you to balance your resources against your goals
and to design a test that you can trust and that costs no more than necessary.
Power Curves graph the dynamic relationships that define power, which reveals
the big picture and ensures that no option escapes your consideration. And,
perhaps most importantly, Power Curves make power analysis an easier and
more accessible part of every project. Empower your test. Trust your results.